Report on Measuring New Zealand’s Productivity

Keywords: Growth & Innovation;

Executive Summary

The Department of Labour commissioned this study to give further consideration of the Diewart and Lawrence output series, reported in Measuring New Zealand’s Productivity (D&L (1999), called here D&L99. This exploration data base raises two issues.

Construction of the D&L Series

The first is that they have appeared to construct a data base parallel to official and semi-official ones. Initially they did this because in their tax investigations required them to use expenditure aggregates at factor prices. However there is not the same need to do so for investigating productivity changes. Typically New Zealand economists have built data bases complementary to (rather than parallel to) the official ones (although sometimes Statistics New Zealand (SNZ) develops the parallel series at a later date, so there can be an overlap). The big data bases, such as the RBNZ and the RPEP, have detailed documentation of their construction.

It is also worth noting that there is a constant process of quality assessment of SNZ series, not only within the department, but from the actions of those outside who have used the data (often for macroeconomic forecasting), and informally discussed the results with SNZ. It is these processes of quality assessment (and the professionalism of those involved) which gives some confidence in the SNZ series, although obviously there are problems, and all the series are subject to noise larger than their users would like.

With the exception of the private and public (market) consumption series, which were provided by SNZ, D&L constructed their own component series which parallel to official and semi-official data. They do not seem to have attempted any reconciliation between them, their documentation of the construction is poor, and while they are likely to have had their own internal quality checks, quality assessment has not, thus far, been nearly as comprehensive as the official series.

It should be added that D&L are to be applauded for having obtained the SNZ consumption series, which were not previously in the public domain. With hindsight it is disappointing that they did not do this for the other components of their output measure. One would urge SNZ to push back their volume expenditure series which starts in 1983/4 as far as possible, and at least to 1971/2 when the consumption series starts. However it seems likely that an authoritative volume stock series would not be available before 1977/8. In that year a new commerce inventory series was introduced, which appears to overlap badly with the previous one, making it difficult to construct a consistent series.

Reliability of the D&L Series

How reliable is the D&L series? We can compare it with the parallel SNZ series (and where they do not exist, with hybrid ones constructed using official and semi-official data). On the whole the D&L series are not too unsatisfactory, except in the following respects:
– they are much more volatile;
– the secular story they tell is of slower growth before 1982/3 and faster growth after.

These differences (defects?) arise mainly from the sheer difficulty of the construction of the stock change series (which seems to be involved in every one of the unorthodox swings in the D&L business cycle), and some problems in the GFCF deflator, especially in the early 1970s. There may be other problems but they are swamped by the two identified here.

In summary, there is no reason to assume that the D&L series are superior to the SNZ based ones, while it seems likely that it is possible to construct superior expenditure side series before 1982/3 (of which GDPM(X) is an example, although it can be improved).

The Usefulness of the D&L Series

I give no opinion about the usefulness of the D&L data base in regard to their tax work, having not assessed it for this purpose. In regard to productivity measurement, it seems to me that the D&L data base adds little to that which we already have. In particular the high volatility means it cannot be adjusted to a cyclically neutral basis. The method used on page 29 of D&L99 is embarrassingly crude. Yet, other than using a three (or longer) year moving average, there is probably no better way, given the noise in the data base.

Can its long term secular trends be trusted? They are not that different from the official trends. Insofar as they are, that appears to be a function of the oddities of the GFCF deflator and the artificial volatility of the series arising from its stock change component. In particular I would be reluctant to use this series to demonstrate there has been an acceleration in the growth of productivity. Its conclusion to this effect seems far to dependent upon the faulty GCFC deflator series. (In any case insofar as it provides evidence, any acceleration began in the early 1980s, rather than the mid 1980s or 1990s, following the reforms.)

As a final caution, the difficulties in the GFCF deflator probably also undermine the reliability of the capital input index, although I have not investigate this in any detail.

Summary Conclusion

The ultimate test is that having spent a number of weeks investigating the series, would I use the D&L series for any investigation of the long term behaviour of the New Zealand economy? My short answer is no. There are better series in existence or easily constructible. I would use the consumption components of the D&L series, since they are based on official data, and I perhaps would use the D&L series as a cross check on any preferred series I was constructing or using. With those exceptions I would be reluctant to place any great weight on the D&L series.

Summary of Individual Sections

1. The report begins by describing briefly the measurement framework that was used, and some of the key notions.

2. D&L99 compute an expenditure side estimate of GDP excluding non-market expenditures (public sector net output and the imputed rent on owner occupied housing) for the period 1971/2 to 1998/9 in value and volume terms.
The construction of the output data in the report is poorly documented.

3. A comparison between the D&L99 and the SNZ market GDP series (measured at factor cost), shows the D&L series averaging 6.3 percent lower than the SNZ series. The gap was reduced to 4.0 percent if stock changes were excluded from both series. The correlations between the series on a levels and year-by-year (percent increase) basis are highly significant for the measure without stock change, and between levels for the measures with stock change. (The year-by-year correlation is markedly lower, although still statistically significant.)
In summary the D&L nominal series corresponds broadly, but not exactly, to the official SNZ series. The most problematic match is between the stock change series.

4. D&L derive their consumption components directly from SNZ. These are not given further consideration in the study.
A comparison of the D&L price deflators for exports and imports of goods and services with the SNZ one from 1982/3 (it is not available before) and the RBNZ before that date suggests the match is satisfactory.
However a comparison of the D&L deflator for Gross Fixed Capital Formation suggests it correlates poorly with the SNZ series (available only after 1982/3), and also with the RPEP and RBNZ series which go back to an earlier date. The fit is poorest up to 1983/4, especially in the early 1970s, where the D&L deflators seem far too high, relative to their later levels. (This means the D&L deflators rise more slowly than the official ones, so their real investment expenditures rise more quickly. The effect is to give later GDP growth a boost.)
In summary, the D&L external deflators are satisfactory, but the investment deflators are not, especially in the earlier part of the period.

5. Stock change figures are problematic in New Zealand before 1977/8 (when SNZ does not even provide an inventory valuation adjustment in its nominal national accounts), while SNZ volume figures are not available before 1982/3. In any case the stock change figures are the most problematic component of any expenditure side estimate of net output.
Following a detailed analysis, the study concludes that it is not possible to have any confidence in the real stock change series reported in D&L (1999). It is not clear how it was constructed, it does not appear to be comprehensive, there is some problem with the deflators (or perhaps the fundamental construction), and the series does not correlate with any other plausible alternate series.

6. The report examines five measures of net output:
GDP(P) The SNZ volume estimate of GDP based on the production side.
GDPM(P) The net output of the market sectors of the economy (i.e. Market GDP) constructed from SNZ data.

GDPM(X) This hybrid series of net market output measured on the expenditure side consists of splicing the SNZ market output series from 1982/3 to a composition of volume expenditure components before then.
D&LC(onstructed) This series was constructed from the individual components reported in D&L(1999).
D&LR(eported) This is the output series reported and used in D&L (1999). It differs slightly from D&LC(onstructed).
The D&L series do not match well with the officially and semi officially derived series. The best match is after 1982/3. The D&L series are also more volatile (measured by the percentage deviation of the percent annual increase). The trend patterns are also different. D&L has lower trend growth rates in the 1970s and higher in the 1980s.

7. It was only possible to compare the components of the GDPM(X) with D&LC, and their consumption components are identical. Moreover, the stock change estimates were not comparable. The GFCF and external components comparisons proved reasonably satisfactory, although there were important differences in trends. A curiosity is that although the GFCF value and price series were poorly correlated, the volume series from the two sources showed a similar cyclical pattern (but a different secular one).

8. Following a consideration of years in which there are large swings suggests that the both D&L series is much more volatile than the market output GDP and the hybrid expenditure series: probably misleadingly so. The very early difficulties appear to reflect the problems D&L have with their GFCF deflator. Over the entire period the inventory cycle seems to be problematic. In no case of a business cycle does the D&L series appear to tell a better story of the period than the more officially based data.

TABLES

Table 1: Comparison of D&L and SNZ Market GDP (1984/5)

Table 2: Correlations between D&L and SNZ Nominal GDP Series

Table 3: Comparisons between D&L and SNZ External Price Series

Table 4: Correlation between D&L, SNZ, RPEP, and RBNZ GCFC Deflators

Table 5: Correlation Between D&L and RBNZ Stock Levels

Table 6: Comparisons between Various Real GDP Series
6a: 1971/2-1997/8
6b: 1982/3-1997/8
6c: 1971/2-1982/3

Table 7: Comparisons between D&LC and GDPM(X) for GFCF, Exports and Imports

Table 8: Correlation between GFCF Characteristics (1971/2-1983/4)

Table 9: Years of Major GDP Swings

GRAPHS

Graph 1: D&L and SNZ Nominal GDP Series
1a: With Stock Change
1b: Without Stock Change

Graph 2: D&L, SNZ, RBNZ, and RPEP GFCF Deflator Series

Graph 3: D&L, RBNZ, and SNA Stock Change Series.

Introduction

The Department of Labour commissioned this study to give further “consideration of the Diewart and Lawrence output series [reported in Measuring New Zealand’s Productivity (D&L (1999), called here D&L99 etc]. In particular … we were interested in the major fall in the output index between 1974 and 1975 (-12%) and the major rise between 1983 and 1984 (+14%).”¹ I have interpreted the remit a little more widely, not only to evaluate the cycle and noise, but also to look at the secular usefulness of the data. ²

1. Measuring Output

By way of background, it is to be recalled that economists measure economic output by the total production of goods and services in the designated region (i.e. New Zealand) valued in transaction prices. The underlying framework is the national accounts.

The core notion is the aggregate of net output. In order to avoid double counting from the output of one firm going into the input of another, the value of the inputs are deducted from the value of gross output.

In principle there are three main ways of measuring this output:
– the expenditure method (“side”) measures what is finally purchased (or goes into inventories), deducting imports since they are inputs not produced locally;

– the production side measures the net output of firms aggregated into sectors;

– the income side measures the incomes which the production process generates, since the sum of the incomes has to equal net output.
In principle the three totals measure exactly the same thing, and should have the same quantity in each year. Practically there are measurement errors (the “statistical discrepancy”).

Historically, Statistics New Zealand (SNZ) relied upon an incomes side approach (this is called ONA – old national accounts), matching it to an incomplete expenditure side (private consumption was a residual). In the 1970s it switched over to the recently introduced UN System of National Accounts (SNA) with a focus of a production side estimate. There are “official” national accounts in SNA definitions on the income and expenditure sides going back to March year ending 1962 (the New Zealand convention is to call this the 1961/2 year). (SNZ 1997) However previous to 1971/2 these are less reliable, and less detailed. Further major improvements were introduced from the 1977/8 year, and the expenditure side becomes more elaborate from 1983/4.

A particular problem arises from changes in prices, especially given the marked inflation in the 1970s and 1980s. Typically, the components of the national accounts are estimated in value (i.e. current price) terms, and are then deflated (using a suitable price index) to volume or constant price terms. Another common terminology is the value series is called “nominal” and the volume series “real”.

The aggregates may be valued in market prices which incorporate indirect taxes and subsidies, or factor (or producer prices) which do not. The SNA data is usually in market prices, whereas D&L use factor prices (which complicate the comparison). The difference hardly matters for the real series, since the deflation adjusts for changes in indirect taxes and subsidies. ³

Official volume estimates in an SNA format go back to 1971/2 on the production side, but only 1983/4 on the expenditure side. The Research Project on Economic Planning provides volume production side estimate back to 1954/5, and there is an SNZ estimate of total volume GDP going back to that year too. Series of unofficial estimates of aggregate production (value and volume), of varying reliability, go back into the nineteenth century.

2. Constructing the Output Data Series

D&L99 do not provide an account of how its output data series were constructed but its writers say they have “updated, expanded and further improved the detailed data base first developed in Diewart and Lawrence (1994, 1998).” (p.13) These earlier studies were primarily concerned with the incidence of taxation and the resulting consequences, whereas D&L99 is concerned about the measurement of total factor productivity. It may also be that the improvements refer to the input series, a conclusion consistent with D&L99 making no further reference to changes in the output series. The output data in D&L99 appears to be the same as in D&L98, except for the addition of the 1995/6 to 1997/8 years.

Regrettably, the discussion on the data construction in D&L94 is superficial, and in D&L98 is not comprehensive. As best as I can interpret from the published sources:
– The output data covers only market production on a GDP basis. This is elaborated in a following section.
– The data is measured at producer prices, rather than the more common market prices. As already explained this distinction is not so important after deflation.
– The data refers to March year, not calendar year, even when there is no indication in the text or tabulation. ⁴
– The data is constructed on an expenditure side basis.
– Some data was provided by Statistics New Zealand (SNZ) (private and public consumption), the remainder seems to have been calculated by the consultants, usually from official or semi-official sources.
– There is little detail of how the less official data was calculated. For instance in D&L98 the section on exports and imports amounts to 8 lines, and there is no reference to services. Investment goods (i.e. gross capital formation) has 23 lines, but there is no reference to inventory changes. There is more discussion on the inventory in D&L94 but, as reported below, that proves problematic.
– There is no explanation of how the components of the expenditure data are aggregated to the total output index. As reported below, I have been unable to reconcile the sum of the reported component outputs with the total output index.

In summary, the construction of the output data in the report is poorly documented. Those wishing to use the data should be aware that they are very dependent upon the competence of the authors. Independent verification of the data, other than that which comes direct from SNZ sources, has not been possible.

3. The Nominal Market Output Series

Because D&L work with an output series which covers only market production and which is valued in producer prices, their series is different from the conventional GDP measure which includes some other economic activities, and taxes and subsidies. In principle the conventional nominal measure can be put on the same market basis as the D&L99 measure by deducting indirect taxes, adding subsidies, and deducting the sectoral activities they define as non-market. D&L provide no comprehensive account of the sectors they include, but their non-market sectors are probably the public sector and the imputed rent on owner occupied housing (which is a component of private consumption). On this basis the nominal D&L estimate can be compared with the nominal official estimate.

An example for the 1984/5 (mid year of the D&L series) follows:

Thus there is a difference between the two estimates of $1,741m or 6.3 percent of the official estimate. ⁶ Part of the difference is explained by different estimates in changes of stocks, an issue which has its own section. If the stock change is deducted from each estimate, ⁷ the estimates become $29,256m and $28,552m reducing the discrepancy to $704m or 2.4 percent.

For the 27 years in total, the difference of the output with stock changes ranges from 0.0 percent to 16.0 percent, with an average of 6.3 percent. Without the stock change included, the range is 0.6 percent above to 7.4 percent below, averaging 4.0 percent. ⁸

I also calculated the correlation coefficients between the series. Their high levels may mislead, because there is a strong trend from inflation (and to a lesser extent volume growth), so a correlation between annual percentage changes is also shown. The lower correlations for nominal GDP including stock change indicates that inventory change is an important source of measurement volatility between the series. The high rates between the GDP excluding stock changes, especially for the increase, suggest they are basically the same series.

In summary the D&L nominal series corresponds broadly, but not exactly, to the official SNZ series. The most problematic match in stock change.

4. Converting from Value to Volume: The Deflator Series

The standard way of converting the aggregate from a current price (value) to a constant price (volume) series is to deflate the value series by a suitable price index. ⁹ D&L99 report 48 components to their series:
– 18 components of private consumption on consumption;
– 1 government intermediate spending;
– 6 components of fixed investment (including government investment);
– 2 (an agricultural and nonagricultural) inventory series;
– 11 components of exports (one of which was service exports);
– 10 components of imports (one of which was service imports). ¹⁰

Data on the first 19 (consumption) series was provided by SNZ, and may be taken as consistent with the official data. The remaining series were collected largely from official sources, but were subsequently processed. This introduces a source of potential error.

Exports and Imports

The D&L external series were compared with the
i) the comparable SNA implicit deflator from 1982/3 (when it first becomes available) to 1997/8. ¹¹
ii) the comparable RBNZ implicit deflator from 1971/2 to 1980/1. ¹²

I have used three simple measures to compare the series:
– the average increase over the period;
– the correlation between them, for levels and percentage increases.

A curiosity of the analysis is that strictly we are comparing official and semi-official price indexes which include indirect taxes (and subsidy), with D&L indexes which exclude indirect taxes. The good correlations suggests that there is not a substantial tax element in the values. ¹³ The match between the series for either period is broadly satisfactory.

Gross Fixed Capital Formation

The relative capital formation deflator proved more problematic. On the three compass principle, ¹⁴ it was necessary to look at two alternative series (in addition to the SNZ one). A complication is that they are over different periods. The series that were compared were:
i) the D&L (implicit) aggregate capital formation deflator available from 1971/2 to 1997/8.
ii) the comparable SNA implicit deflator available from 1982/3.
iii) the comparable RBNZ implicit deflator available from 1971/2 to 1993/4.
iv) the comparable RPEP implicit deflator available from 1971/2 to 1996/7.

In order to simplify the presentation, we report here summary statistics between each series for as long a period as possible. They are shown below (with the number of observations in brackets):

While the RBNZ and RPEP series are reasonably closely aligned even on a percentage change basis, and correlate well with the SNZ series, the D&L series appears to be the odd one out. (An eyeball comparison shows that the there is a particularly poor fit in the early 1970s, with the match remaining poor until 1983/4.) The poor correlation before the official series was constructed should come as no surprise to those who have worked in this area. The gross fixed capital formation deflators have always been among the most problematic to construct, and both the RBNZ and the RPEP research groups are among New Zealand economists who have put an enormous effort into providing quality indicators. ¹⁵ Of course the two series may be constructed on largely the same data and assumptions. But they were constructed independently in two research programs, by researchers experienced with the New Zealand data and the New Zealand economy, and at least intuitively will have checked their results against other indicators of the New Zealand economy of the time. Thus D&L deflator has to be considered less reliable than either of these two.

The issues raised early of the effect on the comparisons of indirect taxation on exports and imports also applies here. The implications of the differences in deflators on the output estimates appears later. However it should be noted that unsatisfactory gross fixed capital formation deflators will also impact upon the estimates of real capital stock. Given the deflators are high in the earlier period, the effect will be to raise TFP growth in the 1970s.

In summary, the D&L external deflators are satisfactory, but the D&L investment deflators are not, especially in the earlier part of the period.

5. Stock Change

It is clear that the D&L have difficulties in regard to their stock change data, although it should be added that these are always even more problematic than the GFCF data, as the subsequent discussion will show.

The first difficulty is that the D&L series is not comprehensive. By their account they cover only livestock, and stocks of materials and commercial stocks (finished goods in manufacturing, retail stocks and the narrow definition of wholesale stocks). (D&L94:101-2) A major exclusion is forestry stocks (which fortunately grow fairly steadily), but there are also some minor stocks omitted. In addition SNZ makes adjustments between its stocks and other expenditure, most notoriously in regard to exports, because goods which cross the wharves (and are measured at this point as doing so) are not deemed exported until they are sold. I the interim they are transferred from exports to stock changes. Thus a number of items in the SNA definition of inventories are omitted.

The price deflator reportedly used to deflate the commercial stocks was the price index for all New Zealand industry inputs (excluding labour), implying there was no disaggregation. In any case the price index does not match the actual content of the stocks well, increasing too quickly, and thereby depressing real stock levels at the end of the period, and stock growth through it. Indeed the D&L series shows a decrease in aggregate stock levels between 1971/2 and 1990/1, which seems most unlikely (and is not replicated in any other available series).

The second difficulty is that while the D&L nominal stock change in the 1971/2 year is reported as $95m for their agricultural (livestock?) stock change and -$57m for their nonagricultural stock change, the value in 1971/2 prices is reported as $79m and -$61m respectively. Although as explained below, price deflators for stock change are problematic, they should be at unity in the base year. Here they are not.

Third, the data reported in D&L99 does not appear to be consistent with that in D&L94, but there is no further comment on data construction thereafter, so further investigation is not possible.

To understand the difficulties with the stock change, consider a simple inventory with a well defined price. Suppose its value is S_t at the beginning of period t, when the price level is P_t. The apparent increase in the value of stocks in the period t is given by

S_t+1– S_t

.
However, for national accounts purposes, which focuses on the growth of production, the effect of inflation in the increase in the value of the stocks is not a part of production. Assuming that the stocks are valued in current prices, than the increase in stocks from additional production is

S_t+1/(P_t+1/P_t) – S_t

at the beginning of the period prices. The difference between the two,

S_t+1(1-P_t/P_t+1),

is called the “inventory valuation adjustment”.¹⁶ Until 1977/8, the SNZ national accounts did not have an IVA.

To calculate the real increase in stocks, we divide the nominal value of each stock level by the price level (assuming that the base price level is set at 1.0). ¹⁷ The difference between them is the real increase, or in period t

S_t+1/P_t+1 – S_t/P_t,
or
{S_t+1/(P_t+1/P_t) -S_t}/P_t.

Thus the real increase is the SNA nominal increase divided by the price index at the beginning of the period.

However, once aggregation occurs, with the procedure being applied to a number of types of stocks each with their own price index, the simplicity of these formula disappears following aggregation. In principle this also happens for any other aggregation, but providing the price changes are all the same sign, and their increases of similar magnitude, the situation does not usually cause problems. However, because typically the components of the aggregate stocks series are both rising and falling, the aggregate nominal and real series do not follow one another well. For instance the nominal increase may be positive but the real increase negative, so the apparent implicit price deflator is negative.¹⁸

This meaningless of the aggregate implicit price deflator, means that we cannot compare the price deflators for aggregate stock change. Instead I have made a direct comparison of four estimates of the real stock change:
– SNZ: the official SNA series. (1982/3-1997/8);
– RBNZ: the series from the RBNZ data base. (1971/2-1994/5);¹⁹
– D&L94: I constructed this series from the data reported in D&L94. (1972/3-1990/1);²⁰
– D&L99: as reported in D&L99.

Because we cannot standardise them to the same price base (other than by disaggregating into components, which is not possible given the lack of data), the best way of comparing the series is by correlation. The results are tabulated below with the number of observations next to the correlation coefficient.

The only statistically significant correlation is between RBNZ and D&L94, probably because they are both dominated by commerce stocks. None of the unofficial series correlate well with the official ones, and the two D&L series do not correlate significantly either.

A weakness of the correlation approach is that it does not assess secular trends. Thus the correlation between the RBNZ and the D&L94 series is partly misleading because they have quite different long run properties. In particular, the RBNZ inventory stock measured in 1971/2 prices rises 68.9 percent between end March 1972 and end March 1991, whereas D&L94 falls 5.6 percent over the same period. The latter pattern seems unlikely, and probably reflects a faulty deflator for the commerce stocks.

In conclusion, it is not possible to have any confidence in the real stock change series reported in D&L99. It is not clear how it was constructed, it does not appear to be comprehensive, there is some problem with the deflators (or perhaps the fundamental construction), and the series does not correlate with any other plausible alternate series. (We will see its weaknesses playing a key role in later problems with the aggregate D&L output series.)

6. Comparing and Constructing the D&L Output Series

This report compares five series:

1. GDP(P)
This is the SNZ volume estimate of GDP based on the production side. It is the most used measure of changes in economic activity. We would expect this to be less volatile/cyclical than the market concept that D&L use, because the non-market sector is less cyclical.

2. GDPM(P)
This consists of the net output of the market sectors of the economy (i.e. Market GDP). It was constructed by subtracting the net outputs of the general government and owner occupied housing sectors from GDP(P). This series is the production side estimate of the market output concept used by D&L.

3. GDPM(X) (a.k.a the “hybrid” series)
This series, which is an expenditure side estimate of market GDP based on New Zealand sourced data, consists of splicing two series together. The more recent series was the SNZ economy wide output series on the expenditure side less the expenditures on (which are also the outputs of) general government and owner occupier housing, again converting the aggregate into a measure of market output. However this series goes back only to 1982/3.

Before then, back to 1971/2, I constructed a market output series from the expenditure side as follows.
– private and public consumption: The SNZ data provided to D&L;
– gross fixed capital formation: SNZ nominal GFCF deflated by a geometric average of the RBNZ and RPEP GFCF deflators;
– stock change: annual changes in the volume RBNZ inventory stock series (scaled to the 1982/3 SNZ estimate).²¹
– exports: the SNZ series of the total export volume index the reported in SNZ(1986/7). However this only covers goods. A comparison of the volume exports goods and volume export services series for the 1982/3 to 1997/8 period suggests they remained in a relatively fixed proportion, and that was assumed before 1982/3.²²
– imports: the SNZ series of the total import volume index the reported in SNZ(1986/7). However this only covers goods, so the trended ratio between goods and services was projected back before 1982/3.²³

The resulting series is of a rather mixed ancestry.²⁴ Note that it and the next two have considerable commonality in that the consumption data comes from the same SNZ source.

4. D&LC(onstructed)
This series was constructed by adding the volume expenditure components (subtracting of imports) from Table 38a of D&L99.

5. D&LR(eported)
D&L99 report a (market) output series in their Table 3.1. One might expect it to be exactly the same as the D&LC(onstructed) but it is not. No explanation is given why they are different (although they are obviously closely statistically related).

1971/2-1997/8

Measures for comparing the series over the 1971/72 to 1997/8 period are given in the following table. (The standard deviation of the percentage increase, essentially a measure of a variation about the series trend, will be used in a later section).

Focusing on the percentage change correlations, we can see that the two production side series (GDP(P), GDPM(P)) are closely related,^25> as are the two D&L series (D&LC, D&LR). This is not surprising, given their construction. The hybrid expenditure side series, GDPM(X), appears to correlate reasonably well with both groupings.²⁶

Recalling that the hybrid series was constructed quite differently before and after 1982/3, and that generally the quality of the data base is superior after that date, the two sub-periods were checked separately. First consider the later series (form 1982/3), with its better quality data.

1982/3-1997/8

The measures for comparing the series over the 1982/3 to 1997/8 period are given in the following table

The separate grouping of the two production side and the two D&L series remains, although now even their increases correlate significantly.²⁷ The GDPM(X) series joins the production side group (satisfyingly because they are all, in effect, official SNZ series).

1971/2-1982/3

The measures for comparing the series over the 1971/72 to 1997/8 period are given in the following table.

The grouping of GDP(P) and GDPM(P) and of D&LC and D&LR are again maintained, but on the basis of the correlation between their increases they are different series measuring quite different phenomenon. This time GDPM(X) appears to have more in common with the D&L series and little with the production side estimates.²⁸ This is not so surprising in that the D&L and GDPM(X) series have their consumption components in common. However it is disappointing that GDP(M) appears to have little short run relation to the production side estimates. One suspects that a better estimate may be possible.²⁹

(Note the different stories the series are telling about the patterns of secular trends. The production side estimate of market GDP has it growing 1.9 percent p.a. in the earlier period, and 2.4 percent p.a. in the later period, a rise of .5 percentage points The expenditure side estimates have lower growth in the earlier period (1.3-1.5 percent p.a.), and a higher one in the later period (2.5-2.8 percent p.a.) giving an increase of 1.2 to 1.5 percentage points, or more than double the production side change. Thus the story one may tell can be varied by suitable choice of the data series.)

The D&L series do not match well with the officially and semi officially derived series. The best match is after 1982/3. The D&L series are also more volatile (measures by the percentage deviation of the percent annual increase). The trend patterns are also different. D&L has lower trend growth rates in the 1970s and higher in the 1980s.

7. Comparing the Year to Year Changes by Components

It is only possible to compare the components of GDPM(X) with D&LC, since there is no expenditure side aggregation available for any of the other series. Moreover, two of the components, private and public (market) consumption are identical, while it is simply not possible to compare the stock change series.³⁰ Again I have used the mean changes and correlation of levels and percentage increase method.

The two export series show a close similarity over the whole period (although there is a different pattern between the sub periods, which may be an endpoint problem). The two import series are very similar in the post 1982/3 period, but a substantial trend divergence before (which is also reflected in the correlation coefficients).

However the relationship between the Gross Fixed Capital Formation series is odd. Again the post 1982/3 fit is good, but in the earlier period shows a substantial divergence in trend, together with a statistically insignificant (at the 5 percent level) correlation between levels. However there is a strong correlation between the increases. An examination of the value and price data shows the following:

It appears that the while the value and price indexes correlate well at the series levels, their ratio does not. However, while they correlate poorly as percentage increases, their ratio the series increases correlate exceptionally well. The D&L description of how they constructed their investment goods data is brief. But D&L98 mentions that much of the data came from The Treasury. It is possible that the Treasury data came from the sources we used to construct the GDP(M) (volume) series. However, without examining the D&L worksheets it is not possible to explain why the underlying series diverge so greatly, why there is substantial differences in the trends of the volumes series, and yet why their cyclical patterns are reasonably close.³¹

It was only possible to compare the components of the GDPM(X) with D&LC, and their consumption components are identical. Moreover, the stock change estimates were not comparable. The GFCF and external components comparisons proved reasonably satisfactory, although there were important differences in trends. A curiosity was that while the GFCF value and price series were poorly correlated, the volume series from the two sources showed a similar cyclical pattern (but a different secular one).

8. Cyclical Swings and Errors

The terms of reference specifically asked to look at some of the sharp annual swings that occurred in the D&L series. However the New Zealand economy is subject to actual cycles, which is one of the sources of GDP growth swings. In order to accommodate this we have examined only the extreme annual percentage changes which were identified as follows. The four series of section 6 (excluding GDP) was separated into the two sub periods, and detrended. The GDPM(P) series, probably the most accurate, experienced a standard deviation about its trend of 3.0 percentage in the pre 1982/3 period and 2.6 percentage points after 1982/3. Swings from the trend which were greater than 6.0 percent in the earlier period and 5.2 percent in the second are listed as follows (the percentage increase being shown – brackets indicates it was inside the range):

In total this identifies 11 of the 26 possible years.

However we may dismiss the 1993/4-1995/6 period as the series are telling the same story. It was an exceptional boom.

One might be inclined to dismiss the first four year period, 1971/2-1975/6 on a similar basis. It is certainly true that all series show a strong expansion in the first couple of years, although GDPM(P) locates the peak a little later than the expenditure side series. However in the second two years of the period the D&L series tell quite a different story, of a wild downswing in 1974/5 followed by an almost as spectacular recovery. This is not evident in the other two series, in other indicators, nor in contemporary commentary. This is not merely a matter of timing, because the D&L series appear to be growing faster over the period. Inspection suggests that the faulty GFCF price deflators is interacting badly with the also fluctuating level of investment. (There may also be inventory problems, a caveat always with the D&L series.) In summary, it seems unlikely that the D&L series are well representing either the cycle or the trend over this period.

The D&L series have a mini bust and boom in the 1978/9-1980/1, again not evident in the other series, in other indicators, or in contemporary comment. The difference appears to be in contrary stock cycles between GDPM(X) and D&LC. Given the difficulties with inventory measurement there is little more to be said.

The 1982/3-1984/5 period also has different profiles of a cyclical between the GDPM and D&L series. Again the latter do not seem to conform to other indicators or the conventional wisdom, and again the inventory cycles between GDPM(X) and D&LC are quite different. However this time the GDPM(X) stock change data is based on the official (and very detailed) estimates, and may be taken as more authoritative.

Undoubtedly there was some contraction in the 1988/90 year. However The D&L contraction seems far too strong, and again the profiles in the stock cycle are quite different.

In summary, the D&L series is much more volatile than the other two series – probably misleadingly so. The very early difficulties appear to reflect the problems D&L have with their GFCF deflator. Over the entire period the inventory cycle seems to be problematic. In no case does the D&L series appear to tell a better story of the period than the more officially based data. ³²

Conclusion
The detailed conclusion is in the executive summary. In summary:

The ultimate test is that having spent a number of weeks investigating the series, would I use the D&L series for any investigation of the long term behaviour of the New Zealand economy? My short answer is no. There are better series in existence or easily constructible. I would use the consumption components of the D&L series, since they are based on official data, and I perhaps would use the D&L series as a cross check on any preferred series I was constructing or using, but with those exceptions I would be reluctant to place any great weight on the D&L series.

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Bibliography
Diewert, E. & D. Lawrence (1994) The Marginal Costs of Taxation in New Zealand, Swan Consultants, Canberra (prepared for the New Zealand Business Roundtable). a.k.a. D&L94.
Diewart, E. & D. Lawrence (1998) The Effects of Capital Taxation in New Zealand, Tasman Asia Pty Ltd, Canberra (prepared for the Institute of Policy Studies). a.k.a. D&L98.
Diewart, E. & D. Lawrence (1999) Measuring New Zealand’s Productivity, Diewart Enterprises Ltd (prepared for Department of Labour, Reserve Bank of New Zealand, and The Treasury). a.k.a. D&L99.
Easton, B.H. (1997) In Stormy Seas: The Post-War New Zealand Economy, Otago University Press, Dunedin.
Easton, B.H. (1999) Commentary on “Measuring New Zealand’s Productivity” paper for Seminar on New Zealand Productivity, March 25, 1999, Economic And Social Trust on New Zealand paper 99.9, Wellington.
Philpott, B.P. (1999) Deficiencies in Diewart-Lawrence Capital Stock Estimates, RPEP Paper 294.
Statistics New Zealand (1999) Chain Volume Measures in the New Zealand National Accounts, Wellington. (This is the latest relevant publication. Various other SNZ sources were used to supplement it.)

Endnotes
1. Letter from S. Chapple, 9 April 1999.
2. Philpott (1999) has evaluated some aspects of the D&L capital series.
3. There is a very small divergence arising from the base shares differing, insofar as the taxes and subsidies are in different proportions on different components. this rarely affects aggregate indexes calculated by the overall results by a significant amount.
4. See D&L98 which, however, includes the mysterious statement “[r]ecently there has been a move to present New Zealand data more consistently (sic) on a June year basis.” (p.71)
5. This is the expenditure side estimate.
6. D&L do not actually give their GDP figure. This is calculated by adding together their figures for the components of consumption (including intermediate government consumption), stock changes, investment goods, exports less imports.
7. There is a slight double counting since taxes and subsidies are attributed to stock change.
8. The SNZ series grow on average 9.8 and 10.0 percent p.a. respectively, while the D&L99 series grow 10.1 and 10.2 percent p.a. This small difference on a year to year basis amounts to up to 8.5 percentage points over the 27 years. Even such a small difference can matter on an annual basis when productivity comparisons are being made.
9. There are a number of detailed options in the application of this approach, which are unlikely to affect the outcomes markedly and are not pursued here.
10. There are three more than D&L98 because of government investment, and other exports and imports being split into services and other goods.
11. The source for this and other data is Statistics New Zealand (1998), which is a chain volume implicit price index.
12. I did not compare with the SNZ deflators for they are for goods only and do not include services.
13. An issue which needs to be worked through is the impact of GST which was imposed on GFCF and imports (which are usually measured at the border exclusive of the GST they incur). I propose to check how SNZ dealt with this when I next talk to them. D&L make no mention of the issue.Endnote 2 may be relevant here.
14. Planes carry three compasses, because when there are only two, one cannot tell which is wrong.
15. Des O’Dea is another who promptly comes to mind.
16. On the incomes side, the IVA is deducted from operating surplus.
17. If the base period is 1, the base price is not P1 in this definition, because that is the price at the end of (not during) the period. A better estimate is usually (P0 + P1)/2, the average of the prices at the beginning and the end of the period.
18. Suppose there were just two stocks, where the nominal increase in the first was $100m and the nominal decrease in the second was $99m, so that the net nominal increase was $1m. Suppose the relevant price deflator for the first stock was 1.02 and for the second was 1.00. In this case the real increase would be 100/1.02 -99/1.00, or -$1m. So the implicit price deflator would appear to be -1.00! This phenomenon occurs in practice, and is one of the reasons that SNZ does not publish an implicit stock change deflator.
19. In fact the data goes back to 1961/2. It is provided as real stock levels, the difference being the real stock change. Note the series, which is primarily used for modelling, does not pretend to be comprehensive.
20. The inventory stock series are described as “March Year”. I have assumed that they are March ended. (D&L94, Tables A.14-17).
21. Given the inherent problems in all stock change series, I may well have been adding noise to the data.
22. The export and import service volume series could be improved with further work. For instance were I constructing my best possible market GDP on the expenditure side I would consider using the D&L service volume series before 1982/3.
23. A comparison of the volume imports goods and volume import services series for the 1982/3 to 1997/8 period showed a reasonably consistent pattern of decline in the proportion (so import services appeared to be growing at .9 percentage points p.a. less than import goods).
24. Because they could be improved, I have not provided a table of the individual components. They are available from the author.
25. I express some satisfaction that the expenditure side series trend a little higher, say .2 percentage points p.a., than the production side series. I argued this was true in Easton (1997) because the expenditure side deflators are likely to better adjust for quality. The observed difference here is of a similar order of magnitude.
25. The critical value for a correlation coefficient at 25 degrees of freedom is .381 at a 5 percent level of significance, and .597 at a 0.1 percent level of significance.
26. The critical value for a correlation coefficient at 14 degrees of freedom is .497 at a 5 percent level of significance, and .623 at a 1 percent level of significance.
27. The critical value for a correlation coefficient at 10 degrees of freedom is .576 at a 5 percent level of significance, and .708 at a 1 percent level of significance.
28. For instance, improving the external services components, and it should be possible to get reasonable estimates of volume stock changes back to 1977/8.
29. I tried a number of ingenious ways, but the underlying problem of the lack of a sensible aggregate deflator series, plus the lack of detail in the data, defeated me.
30. See Section 4 for further discussion on the gross capital formation deflator.
31. One of the Department of Labour commentators provided a very detailed comparison with the QSBO data. It concludes that “examination of the QSBO data does not seem to shake the soundness of the conclusions” drawn here. A copy of this note is available from the author.

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